Question

from a qurdratic polynomial one of whose zeroes is root 5 and the product of zero is - 2 root 5

Answer 1

Answer :

x² - ((5√5 - 2)/√5)x -(10/√5)

Explanation :

let α and β are the zeros of the quadratic equation,

α = 5 and β = ?

As we have given, the product of zeros is - 2√5

so,( α .β)=- 2√5

(5.β)= -2√5

β = -2√5 / 5

=-2√5 / (√5 x √5)

β = -2 /√5

we know the formula to making a quadratic equation, if the roots of the quadratic equation are α and β,

[x² - (α + β)x + (α.β)]

x² - (5 + (-2/√5))x + (5 x (-2/√5))

x² - ((5√5 - 2)/√5)x + (-10/√5)

therefore,

x² - ((5√5 - 2)/√5)x -(10/√5) is the required quadratic equation.